Properties

Label 182.2.d
Level $182$
Weight $2$
Character orbit 182.d
Rep. character $\chi_{182}(155,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

Trace form

\( 8 q - 8 q^{4} + 20 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{4} + 20 q^{9} - 8 q^{10} - 16 q^{13} + 4 q^{14} + 8 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 16 q^{25} - 24 q^{27} + 16 q^{29} + 8 q^{30} - 20 q^{36} - 16 q^{38} + 8 q^{40} + 4 q^{42} + 24 q^{43} - 8 q^{49} - 8 q^{51} + 16 q^{52} - 8 q^{53} + 40 q^{55} - 4 q^{56} - 16 q^{61} + 24 q^{62} - 8 q^{64} - 12 q^{65} - 32 q^{66} + 8 q^{68} + 16 q^{69} + 12 q^{74} - 80 q^{75} - 24 q^{77} - 44 q^{78} - 44 q^{79} + 48 q^{81} + 40 q^{82} + 88 q^{87} - 4 q^{88} + 32 q^{90} + 8 q^{91} - 12 q^{92} + 8 q^{94} + 24 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
182.2.d.a 182.d 13.b $2$ $1.453$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}+2iq^{5}-iq^{6}+\cdots\)
182.2.d.b 182.d 13.b $6$ $1.453$ 6.0.30647296.1 None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(182, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)